On the convergence of solutions of the regularized problem for motion equations of Jeffreys viscoelastic medium to solutions of the original problem (Q950737)

The authors consider the initial-boundary value problems for a viscoelastic medium in an n-dimensional region of Euclidean space. A Jeffreys' type of viscoelastic model is adopted in which linear constitutive relations are between the stress tensor-its material derivative and the strain rate tensor-its material derivative. The existence of material derivatives introduces a non-linearity into inherently linear constitutive relations. By employing properties of Lebesgue and Sobolev spaces and some norm inequalities, the authors prove that weak solutions of initial-boundary value problems for the regularized model converge to weak solutions of original model as the regularization parameter tends to zero. Convergence is stong, weak or \({*}\)weak depending on which function space the solution is imbedded.